DISCRETIZATION OF THE LAPLACE OPERATOR AND THE FAST SOLUTION OF POISSON EQUATION FOR THE EXTERIOR OF A SOLID OF REVOLUTION

When calculating the flow round a solid of revolution at the angle of attack by a beam of charged particles (plasma) moving in a self-consistent electric field, the electric field potential has to be recalculated at each time step, that is, Poisson's equation has to be solved. For the problem to be solved in an acceptable time, a fast algorithm for solving Poisson's equation is needed. An algorithm without saturation is constructed which requires 0 (m2n2 L log3 L) operations, where m, n and L are the number of grid nodes corresponding to the variables r, zeta and phi of a certain curvilinear system of coordinates.